scholarly journals Variational solution of the steady magnetic field distribution in ferromagnetic conductor

2003 ◽  
Vol 16 (1) ◽  
pp. 25-40
Author(s):  
Dragutin Velickovic ◽  
Slavoljub Aleksic ◽  
Zlatica Stojanovic
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Variational Approach ◽  
Normal Component ◽  
Axial Component ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Steady Magnetic Field ◽  
Ritz’S Method ◽  
Magnetic Filed

A distribution of the steady magnetic filed in a very large ferromagnetic conductor of arbitrary, but known cross-section is determined using variational approach with Ritz's method for approximate solving of the problem. Then an axial component of the magnetic vector potential is presented as finite functional series, automatically satisfying boundary condition that the normal component of the magnetic induction on the conductor's surface vanishes. The convergence and the accuracy of the proposed method are investigated. Several results for maps of the force lines and of the inductivity per unit conductor length are compared with corresponding numerical results obtained by Finite Element Method (program package FEMM) and excellent agreement s observed.

Transient magnetic field formulation for solid source conductors

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1539-1545
Author(s):  
Georg Wimmer ◽  
Sebastian Lange
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Numerical Scheme ◽  
Eddy Currents ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Time Step ◽  
Azimuthal Component ◽  
Transient Magnetic Fields

The formulation for the azimuthal component of the magnetic vector potential for axisymmetric magnetostatic applications is well known. However for transient magnetic fields with solid source conductors and eddy currents the formulation has to be revised. A variable transformation is introduced to remove the singularity from the numerical scheme. The numerical error cannot accumulate and is put instead to the postprocessing at every time step.

scholarly journals Voltage induced by currents in power-line sagged conductors in nearby circuits of arbitrary configuration

2015 ◽  
Vol 64 (2) ◽  
pp. 227-236 ◽  
Author(s):  
Krzysztof Budnik ◽  
Wojciech Machczyński ◽  
Jan Szymenderski
Keyword(s):  
Magnetic Field ◽  
Electric Power ◽  
Power Line ◽  
Power Lines ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Inductively Coupled ◽  
The Earth ◽  
Arbitrary Configuration ◽  
Distribution Of Power

Abstract The study presents a calculation method of the voltage induced by power-line sagged conductor in an inductively coupled overhead circuit of arbitrary configuration isolated from ground. The method bases on the solution utilizing the magnetic vector potential for modeling 3D magnetic fields produced by sagging conductors of catenary electric power lines. It is assumed that the equation of the catenary exactly describes the line sag and the influence of currents induced in the earth on the distribution of power line magnetic field is neglected. The method derived is illustrated by exemplary calculations and the results obtained are partially compared with results computed by optional approach

scholarly journals Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

2021 ◽  
Author(s):  
Slobodan Babic
Keyword(s):  
Magnetic Field ◽  
Numerical Integration ◽  
Vector Potential ◽  
Magnetic Force ◽  
Analytical Form ◽  
Mutual Inductance ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Special Cases ◽  
Incomplete Elliptic Integrals

In this paper we give the improved and new analytical and semi-analytical expression for calcu-lating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air. The expressions are ob-tained either in the analytical form over the incomplete elliptic integrals of the first and the sec-ond time or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the special cases when the inclined circular loops are treated. We mention that all formulas are obtain by the integral ap-proach except the stiffness which is found by the derivative of the magnetic force.

The Analysis of Pressure Capability of Different Teeth Structures in Ferrofluid Seal

2010 ◽  
Vol 146-147 ◽  
pp. 1278-1284 ◽  
Author(s):  
Fei Fei Xing ◽  
De Cai Li ◽  
Wen Ming Yang
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Theoretical Model ◽  
Vector Potential ◽  
Potential Method ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Two Sides ◽  
Sealing Gap

Theoretical model of calculating magnetic field of typical ferrofluid sealing structures with magnetic vector potential method is built. Based on the theoretical model, magnetic field distribution of rectangular teeth, two-sides dilated shape and one-side dilated shape teeth structures with common other conditions were calculated using finite element method when the sealing gap was 0.1mm and 0.12mm. The comparison of their results with the same sealing gap showed that one-side dilated shape teeth structure had higher pressure capability than other shape teeth under reasonable design.

NUMERICAL ANALYSIS OF HYSTERETIC LOSSES IN BSCCO/AG TAPES DUE TO TRANSPORT CURRENT AND EXTERNAL MAGNETIC FIELD

2000 ◽  
Vol 14 (25n27) ◽  
pp. 3165-3170 ◽  
Author(s):  
P. LA CASCIA ◽  
L. BIGONI ◽  
E. CEREDA ◽  
F. NEGRINI ◽  
V. OTTOBONI ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
External Magnetic Field ◽  
Time Dependence ◽  
Transport Current ◽  
Magnetic Vector Potential ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Magnetic Vector ◽  
Transport Losses

A model to calculate hysteretic and transport losses in multifilamentary BSCCO/Ag tapes is described. The model considers a rectilinear infinitely long tape and is based on the two-dimensional Poisson equation for the magnetic vector potential. The equation is numerically solved by means of the finite element method. The contribution of both transport current and external magnetic field with any orientation with respect to the normal to the wide side of the tape is taken into account. A sinusoidal time dependence of the transport current and of the external magnetic field is considered but the model can analyze any time dependence of both quantities. A comparison between the calculated and experimental data is reported and discussed.

NEW REPRESENTATION FOR GAUGE-INVARIANT WIGNER OPERATOR OF AN ELECTRON IN A UNIFORM MAGNETIC FIELD

1998 ◽  
Vol 13 (33) ◽  
pp. 2679-2687 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHEN-SHAN YANG
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Uniform Magnetic Field ◽  
Magnetic Vector Potential ◽  
Wigner Functions ◽  
Magnetic Vector ◽  
Ladder Operators ◽  
Gauge Invariant ◽  
Wigner Operator ◽  
Normal Product

By using the technique of integration within an ordered product (IWOP) of operators, we derive the normal-product form of the gauge-invariant Wigner operator of an electron in a uniform magnetic field and its expression in the newly constructed |λ> representation. The virtue of working in the |λ> representation lies in the fact that it is expressed in terms of the ladder operators Π±, K±(see Eq. (10)), thus the magnetic vector potential can naturally be included. On these bases we can easily obtain Wigner functions of some important electron states.

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